Numerical Linear Algebra, Data Mining and Image Processing

In this talk, I will present two applications in data mining and image processing. The first application is related to the problem where an instance can be assigned to multiple classes. For example, in text categorization tasks, each document may be assigned to multiple predefined topics, such as sports and entertainment; in automatic image or video annotation tasks, each image or video may belong to several semantic classes, such as urban, building, road, etc; in bioinformatics, each gene may be associated with a set of functional classes. The second application is related to multiple class image segmentation problem. For example, foreground-background segmentation has wide applications in computer vision (scene analysis), computer graphics (image editing) and medical imaging (organ segmentation). Both applications share the concept of semi-supervised learning and involve several numerical linear algebra issues. Finally, I will present some matrix computation methods for solving these numerical issues. Experimental results are also given to demonstrate the applications and computation methods.